An engineer is designing a cylindrical water tank to hold $5000{\text{ cm}}^3$ of water. Determine the radius of the tank that will minimize the surface area.

• A. $r=5\sqrt[3]{\frac{20}{{\pi }^2}}\text{ cm}$
• B. $r=5\sqrt[3]{20\pi }\text{ cm}$
• C. $r=5\sqrt[3]{20}\text{ cm}$
• D. $r=5\sqrt[3]{\frac{20}{\pi }}\text{ cm}$

Answer: (D)